The cheapest somewhat nearby hotel to the palm DZ is the IBIS al barsha hotel (10-15min cab ride to DZ, cabs are relatively cheap) which if I can recall correctly was around $120 USD a night? Then again that was during New Years for their boogie so I'm sure they hiked up the prices all around?

If you are comfortable with staying in other people's homes, I'd recommend looking into airbnb where you pay significantly less and you usually end up meeting quite interesting people while staying at their home/room for a reasonable price. G'luck finding something and have plenty of fun!